Elliptic curves in class 12.1-d over 4.4.13768.1
Isogeny class 12.1-d contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 12.1-d1
| \( \bigl[a^{3} - 5 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -20 a^{3} + 32 a^{2} + 84 a - 91\) , \( 82 a^{3} - 108 a^{2} - 361 a + 264\bigr] \)
|
| 12.1-d2
| \( \bigl[a^{3} - 5 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{2} - a - 6\) , \( 12 a^{3} - 2 a^{2} - 61 a - 29\bigr] \)
|
| 12.1-d3
| \( \bigl[a^{3} - 5 a - 2\) , \( a^{3} - 2 a^{2} - 4 a + 5\) , \( 0\) , \( -7 a^{3} + 9 a^{2} + 20 a + 6\) , \( -20 a^{3} + 49 a^{2} + 6 a - 4\bigr] \)
|
| 12.1-d4
| \( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - 5 a - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( -126 a^{3} + 190 a^{2} + 540 a - 522\) , \( 907 a^{3} - 1349 a^{2} - 3872 a + 3705\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
